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Abstract
Among connected graphs, some are connected so slightly that removal of a Single Vertex or edge will disconnect them. Such vertices and edges are quite important. A vertexx is called acutpoint inG ifG − x contains more components thanG does; in particular if G is connected, then a cutpoint is a vertexx such thatG − x is disconnected. Similarly, abridge (orcutedge) is an edge whose deletion increases the number of components. As an example, consider the graphs inFigure 3.1; the left-hand graph has cutpointsu andy and cutedgeuy, while the right-hand graph has cutpointx and no cutedge.

Graphs whose cutpoints and cutedges are listed
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Department of Mathematics, Southern Illinois University, Carbondale, IL, 62901-4408, USA
W. D. Wallis
- W. D. Wallis
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© 2007 Second Edition, Birkhäuser Boston
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Wallis, W.D. (2007). Connectivity. In: A Beginner’s Guide to Graph Theory. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4580-9_3
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